Question

Jordan completed the square for the quadratic equation y = 12x² − 2x+3 in order to determine the minimum value of the expression, as shown Step 1: y=12(x²−1x+32) Step 2: y=12(x²−x+14−14+32) Step 3: y=12((x−12)²−14+32) Step 4: y=12((x−12)² +54) Step 5: y=12(x−12)² +58 What mistake, if any, did Sam make?

Answer 1

Jordan made an error while completing the square on the quadratic equation by using incorrect coefficients and constants.

Step-by-step explanation:

Jordan attempted to complete the square for the quadratic equation y = 12x² − 2x + 3. Here are the steps they took, with an analysis of each step:

• Step 1: y = 12(x² − 1/6x + 1/4) (Incorrect, improper coefficient for x term when factoring out the 12)
• Step 2: y = 12(x² − x + 1/12 − 1/12 + 1/4) (Incorrect step of completing the square, the constant term should be (b/2a)² = (1/(2*12))² = 1/576)
• Step 3: y = 12((x − 1/2)² − 1/4 + 1/4) (Correct form of squared term, but incorrect arithmetic on constants)
• Step 4: y = 12((x − 1/2)²) + 54 (Incorrect constant term, as the previous step had errors)
• Step 5: y = 12(x − 1/2)² + 58 (Incorrect final step due to incorrect constant term)

The mistake in Jordan's approach was a combination of using the wrong coefficient for the x term in step 1 and an incorrect method for finding the constant to add and subtract when completing the square, resulting in a miscalculation of the constants in subsequent steps.

Hence, to correct the error, the coefficients should be properly adjusted, the correct constant term (1/576) should be used, and the arithmetic calculations for the constants should be carefully performed again to ensure accuracy.